论文标题
在存在偏见的情况下进行引导推断
Bootstrap inference in the presence of bias
论文作者
论文摘要
我们考虑对（渐近）偏见的估计量进行自举推断。我们表明，即使无法始终如一地估计偏差术语，也可以通过适当的引导程序实现获得有效的推断。具体而言，我们表明，Beran（1987，1988）最初提出的旨在提供更高阶段的细化的方法，通过将原始的自举p值转换为渐近均匀的随机变量来恢复引导有效性。我们提出了两种不同的预分割实现（插件和双引导程序），并提供一般的高级条件，这意味着引导性推断的有效性。为了说明结果的实际相关性和实施，我们讨论了五个示例：（i）基于模型平均的定位参数的推断； （ii）脊型正规化估计器； （iii）非参数回归； （iv）无限方差数据的位置模型； （v）动态面板数据模型。
We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random variable. We propose two different implementations of prepivoting (plug-in and double bootstrap), and provide general high-level conditions that imply validity of bootstrap inference. To illustrate the practical relevance and implementation of our results, we discuss five examples: (i) inference on a target parameter based on model averaging; (ii) ridge-type regularized estimators; (iii) nonparametric regression; (iv) a location model for infinite variance data; and (v) dynamic panel data models.
